Ex.6.4 Q1 Squares and Square Roots - NCERT Maths Class 8

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Question

Find the square root of each of the following numbers by division method.

(i) \(2304 \)   

(ii) \(4489 \)        

(iii) \(3481\)        

(iv) \(529\)    

(v) \(3249\)    

(vi) \(1369 \)

(vii) \(5776\)    

(viii) \(7921\)     

(ix) \(576\)    

(x) \(1024\)   

(xi) \(900\)   

(xii) \(900\)

Text Solution

What is Known?

Perfect squares

What is unknown?

Square root by using division method.

Reasoning:

When a number is large, even the method of trading the square root by prime factorization becomes lengthy and difficult, so the division method is used.

Steps

(i)

The square root of \(2304\) is calculated as follows

Since remainder is zero and number of digits and left in the given number. Therefore,

\(\sqrt {2304}= 48 \)

 (ii)

The square root of \( 4489\) is calculated as follows.

\[\begin{align}\sqrt {4489}  = 67\end{align}\]

 (iii)

The square root of \(3481\) is calculated as follows.

\(\sqrt {3841}= 59\)

 (iv)

The square root of \(529\) is calculated as follows.

\[\sqrt {529}= 23\]

 (v)

The square root of \(3249\) is calculated as follows.

\[\sqrt {3249}= 57\]

 (vi)

The square root of \(1369\) is calculated as follows.

\[\sqrt {1369}= 37\]

(vii)

The square root of \(5776\) is calculated as follows.

\[\sqrt {5776}= 146\]

(viii)

The square root of \(7921\) is calculated as follows.

\[\sqrt {7921}= 89\]

(ix)

The square root of \(576\) is calculated as follows.

\[\sqrt {576}= 24\]

(x)

The square root of \(1024\) is calculated as follows.

\[\sqrt {1024}= 32\]

(xi)

The square root of \(3136 \) is calculated as follows.

\[\sqrt {3136}= 56\]

(xii)

The square root of \(900 \) is calculated as follows.

\[\sqrt {900}= 30\]